Math  /  Trigonometry

QuestionFor Exercises 25-30, assume that θ\theta is an acute angle. (See Example 2)
25. If cosθ=217\cos \theta=\frac{\sqrt{21}}{7}, find cscθ\csc \theta.
26. If sinθ=1717\sin \theta=\frac{\sqrt{17}}{17}, find cotθ\cot \theta.
27. If secθ=32\sec \theta=\frac{3}{2}, find sinθ\sin \theta.
28. If cscθ=3\csc \theta=3, find cosθ\cos \theta.
29. If tanθ=159\tan \theta=\frac{\sqrt{15}}{9}, find cosθ\cos \theta.
30. If cotθ=32\cot \theta=\frac{\sqrt{3}}{2}, find cosθ\cos \theta.

Objective 3: Determine Trigonometric Function Values for Speçal Angles For Exercise 31, use the isosceles right triangle and the 30609030^{\circ}-60^{\circ}-90^{\circ} triangle to complete the table. (See Examples 3-4) 31. \begin{tabular}{|c|c|c|c|c|c|c|} \hlineθ\theta & sinθ\sin \theta & cosθ\cos \theta & tanθ\tan \theta & cscθ\csc \theta & secθ\sec \theta & cotθ\cot \theta \\ \hline 30=π630^{\circ}=\frac{\pi}{6} & & & & & & \\ \hline 45=π445^{\circ}=\frac{\pi}{4} & & & & & -\vdots \\ \hline 60=π360^{\circ}=\frac{\pi}{3} & & & & & & \\ \hline \end{tabular}
32. a. Evaluate sin60\sin 60^{\circ}. b. Evaluate sin30+sin30\sin 30^{\circ}+\sin 30^{\circ}.

Studdy Solution
Evaluate sin30+sin30\sin 30^\circ + \sin 30^\circ:
sin30=12\sin 30^\circ = \frac{1}{2}
sin30+sin30=12+12=1\sin 30^\circ + \sin 30^\circ = \frac{1}{2} + \frac{1}{2} = 1
The solutions to the exercises are as follows:
25. cscθ=72\csc \theta = \frac{\sqrt{7}}{2}
26. cotθ=27217\cot \theta = \sqrt{\frac{272}{17}}
27. sinθ=53\sin \theta = \frac{\sqrt{5}}{3}
28. cosθ=223\cos \theta = \frac{2\sqrt{2}}{3}
29. cosθ=368\cos \theta = \frac{3\sqrt{6}}{8}
30. cosθ=217\cos \theta = \frac{\sqrt{21}}{7}
31. Complete the table using known trigonometric values.
32. a. sin60=32\sin 60^\circ = \frac{\sqrt{3}}{2}
b. sin30+sin30=1\sin 30^\circ + \sin 30^\circ = 1

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